A344529 a(n) is the number of integer quadrilaterals (up to congruence) with integer side lengths a,b,c,d with n = Max(a,b,c,d), integer diagonals e,f and integer area.

0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 4, 1, 4, 0, 0, 6, 3, 0, 0, 7, 8, 3, 0, 5, 3, 8, 0, 1, 0, 5, 5, 3, 10, 0, 10, 11, 5, 5, 0, 3, 5, 0, 0, 11, 0, 11, 18, 15, 5, 0, 6, 10, 0, 6, 0, 26, 4, 0, 11, 1, 32, 3, 0, 10, 2, 10, 0, 10, 12, 17, 34

Offset

1,12

Comments

This sequence is the sum of the sequences A342721 and A342723 which deal with concave and convex quadrilaterals respectively.

Links

Table of n, a(n) for n=1..75.

Formula

a(n) = A342721(n) + A342723(n).

Example

a(4)=1 because the smallest possible quadrilateral is a rectangle with a=c=4, b=d=3, e=f=5 and area 12.

Crossrefs

Cf. A342720, A342721, A342722, A342723, A344528.

Sequence in context: A210209 A328649 A281422 * A144389 A136321 A112987

Adjacent sequences: A344526 A344527 A344528 * A344530 A344531 A344532

Keyword

nonn

Author

Herbert Kociemba, May 22 2021

Status

approved